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If 𝑦¯ = 39.0 (sample mean of variable 𝑦) and 𝑠𝑦 = 18.0 (sample standard deviation of variable 𝑦), find the 𝐳 score of  𝑦1 = 18.0 (a particular observation of variable 𝑦).  Give your answer to 2 decimal places.

Question

If 𝑦¯ = 39.0 (sample mean of variable 𝑦) and 𝑠𝑦 = 18.0 (sample standard deviation of variable 𝑦), find the 𝐳 score of  𝑦1 = 18.0 (a particular observation of variable 𝑦).  Give your answer to 2 decimal places.

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Solution

The z-score is a measure of how many standard deviations an element is from the mean. To find the z-score of a particular observation, we use the formula:

z = (y1 - y¯) / sy

where: y1 = particular observation y¯ = sample mean sy = sample standard deviation

Given in the problem: y1 = 18.0 y¯ = 39.0 sy = 18.0

Substitute these values into the formula:

z = (18.0 - 39.0) / 18.0 z = -21.0 / 18.0 z = -1.17

So, the z-score of y1 = 18.0 is -1.17 (to 2 decimal places).

This problem has been solved

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